Key factors analysis and constitutive equation modification of a macro-NPR bolt for achieving high constant resistance and large deformation characteristics

Abstract A macro-NPR (negative Poisson's ratio) bolt, also called a He bolt, is a composite structure that is composed of two types of steel that are adjusted by design. The mechanical characteristics of the macro-NPR bolt are high constant resistance, large deformation , energy absorption, and impact resistance. In this work, the concepts of a “climbing angle” and a stick-slip element were introduced to analyze the mechanical behavior of the macro-NPR bolt. It was observed that certain bottleneck problems in the existing constitutive model of the macro-NPR bolt had not been solved: (1) The calculation equation of stick-slip displacement included some parameters with weak correlation. (2) In calculating a single stick-slip cycle, the displacement was assumed to be instantaneously completed, whereas the cone sliding process was considered. (3) The random stick-slip phenomenon had a great influence on the performance of the macro-NPR bolt. These problems could lead to significant differences between the existing macro-NPR bolt static tension theoretical curve and the experimental curve. To solve these bottleneck problems, a method to modify the existing constitutive equation of the macro-NPR bolt was proposed in this work, and the modified constitutive equation of the macro-NPR bolt was established to explore the key factors of the macro-NPR bolt to achieve high constant resistance and large deformation characteristics. During static tension, the stress state of the macro-NPR bolt was divided into two stages, an elastic stage and a constant resistance stage. For the constant resistance stage, the stick-slip phenomenon occurred between the cone and the sleeve, whereas the axial force of the macro-NPR bolt was basically constant around P0. Then, using the theory of elasticity and the climbing angle theory, the stress state of the macro-NPR bolt sleeve during tension was solved, and a mathematical expression of constant resistance of the macro-NPR bolt was obtained. Finally, the modified constitutive equation of the macro-NPR bolt was established through the corresponding expression and stick-slip element.